Cloud: BoB
Barrett: Duke
Tifa: Angela
Aeris: Alicia (I think...)
Red XIII: Rastus (not sure if that's right, but it's what I'd use now and might be what I used then)
Cait Sith: Tombo
Vincent: Forgot. Might have been Vincent. *shrugs*
Cid: Cid (HOW CAN YOU NOT?)
Yuffie: Krissy

The chocobos that I remember were called Jax (Gold) and Jake (Black). I think I might've called the Blue & Green ones Sapphire and Emerald, but I'm not sure. I haven't played this game in ages. *just got the PSX version recently, should play it sometime this weekend, hopefully*